Symmetric quivers, invariant theory, and saturation theorems for the classical groups

Understand

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers.

• We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product V_{N\lambda^1} \otimes ...
• \otimes V_{N\lambda^r} contains nonzero G-invariants for some N \ge 1, we show that the tensor product V_{2\lambda^1} \otimes ...
• \otimes V_{2\lambda^r} also contains nonzero G-invariants.